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Math Help - Particle Motion

  1. #1
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    Particle Motion

    A particle moves on the X-axis so that its velocity at any time t is given by v(t)=sin2t. At t=0, the particle is at the origin.

    a.) For 0<=t<= pi, find all values of t for which the particle is moving to the left
    b.) Write an expression for the position of the particle at any time t.
    c.) For 0<=t<=pi/2, find the average value of the position function determined in part (b)

    a.) the particle is moving to the left from (pi/2,pi)
    b.) p(t)=-.5cos(2t)+.5
    c.) 2pi*the integral of sin(2t) from [0.pi/2]

    is that all correct?
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  2. #2
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    Quote Originally Posted by ment2byours View Post
    A particle moves on the X-axis so that its velocity at any time t is given by v(t)=sin2t. At t=0, the particle is at the origin.

    a.) For 0<=t<= pi, find all values of t for which the particle is moving to the left
    b.) Write an expression for the position of the particle at any time t.
    c.) For 0<=t<=pi/2, find the average value of the position function determined in part (b)

    a.) the particle is moving to the left from (pi/2,pi)

    correct

    b.) p(t)= -.5cos(2t)+.5

    correct

    c.) 2pi*the integral of sin(2t) from [0.pi/2] no ...

    \textcolor{red}{\frac{2}{\pi} \int_0^{\frac{\pi}{2}} \frac{1}{2} - \frac{1}{2}\cos(2t) \, dt}
    .
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  3. #3
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    Opps my mistake, thank you so much for pointing it out. I should read more carefully XD
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